Step 1: Understanding the Concept:
Respiratory and photosynthetic electron transport chains utilize mobile lipid-soluble isoprenoid quinones to shuttle electrons between multiprotein complexes.
Step 2: Detailed Explanation:
1. Statement I: Hemoglobin is a specialized respiratory metalloprotein designed for reversible oxygen transport in erythrocytes, and Methemoglobin is an oxidized, non-functional pathological derivative. Neither functions as an electron transport carrier to drive ATP synthesis in mitochondria. Hence, Statement I is false.
2. Statement II: Ubiquinone (Coenzyme Q CoQ) in the mitochondrial inner membrane and Plastoquinone in chloroplast thylakoid membranes are small, mobile, lipophilic benzoquinones with long polyisoprenoid tails that undergo reversible two-electron/two-proton redox reactions ($Q \leftrightarrow QH_2$) to drive proton-motive force generation and ATP synthesis. Hence, Statement II is true.
Step 3: Final Answer:
Therefore, Statement I is false but Statement II is true, matching option (D).